Problem: Simplify to lowest terms. $\dfrac{70}{112}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 70 and 112? $70 = 2\cdot5\cdot7$ $112 = 2\cdot2\cdot2\cdot2\cdot7$ $\mbox{GCD}(70, 112) = 2\cdot7 = 14$ $\dfrac{70}{112} = \dfrac{5 \cdot 14}{ 8\cdot 14}$ $\hphantom{\dfrac{70}{112}} = \dfrac{5}{8} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{70}{112}} = \dfrac{5}{8} \cdot 1$ $\hphantom{\dfrac{70}{112}} = \dfrac{5}{8}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{70}{112}= \dfrac{2\cdot35}{2\cdot56}= \dfrac{2\cdot 7\cdot5}{2\cdot 7\cdot8}= \dfrac{5}{8}$